Properties

Label 1323.2.h.e.226.2
Level $1323$
Weight $2$
Character 1323.226
Analytic conductor $10.564$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1323,2,Mod(226,1323)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1323.226");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.2
Root \(0.500000 + 1.41036i\) of defining polynomial
Character \(\chi\) \(=\) 1323.226
Dual form 1323.2.h.e.802.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.239123 q^{2} -1.94282 q^{4} +(-0.590972 - 1.02359i) q^{5} -0.942820 q^{8} +O(q^{10})\) \(q+0.239123 q^{2} -1.94282 q^{4} +(-0.590972 - 1.02359i) q^{5} -0.942820 q^{8} +(-0.141315 - 0.244765i) q^{10} +(-1.85185 + 3.20750i) q^{11} +(0.500000 - 0.866025i) q^{13} +3.66019 q^{16} +(3.47141 + 6.01266i) q^{17} +(0.971410 - 1.68253i) q^{19} +(1.14815 + 1.98866i) q^{20} +(-0.442820 + 0.766987i) q^{22} +(-2.80150 - 4.85235i) q^{23} +(1.80150 - 3.12030i) q^{25} +(0.119562 - 0.207087i) q^{26} +(0.119562 + 0.207087i) q^{29} -1.66019 q^{31} +2.76088 q^{32} +(0.830095 + 1.43777i) q^{34} +(4.77292 - 8.26693i) q^{37} +(0.232287 - 0.402332i) q^{38} +(0.557180 + 0.965064i) q^{40} +(5.09097 - 8.81782i) q^{41} +(-1.11273 - 1.92730i) q^{43} +(3.59781 - 6.23159i) q^{44} +(-0.669905 - 1.16031i) q^{46} +5.82846 q^{47} +(0.430782 - 0.746136i) q^{50} +(-0.971410 + 1.68253i) q^{52} +(-5.80150 - 10.0485i) q^{53} +4.37756 q^{55} +(0.0285900 + 0.0495193i) q^{58} +2.60301 q^{59} +7.60301 q^{61} -0.396990 q^{62} -6.66019 q^{64} -1.18194 q^{65} +3.50808 q^{67} +(-6.74433 - 11.6815i) q^{68} -8.60301 q^{71} +(7.57442 + 13.1193i) q^{73} +(1.14132 - 1.97682i) q^{74} +(-1.88727 + 3.26886i) q^{76} +7.37756 q^{79} +(-2.16307 - 3.74654i) q^{80} +(1.21737 - 2.10855i) q^{82} +(3.47141 + 6.01266i) q^{83} +(4.10301 - 7.10662i) q^{85} +(-0.266078 - 0.460861i) q^{86} +(1.74596 - 3.02409i) q^{88} +(-1.37360 + 2.37915i) q^{89} +(5.44282 + 9.42724i) q^{92} +1.39372 q^{94} -2.29630 q^{95} +(3.58414 + 6.20790i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 2 q^{2} + 6 q^{4} + 5 q^{5} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 2 q^{2} + 6 q^{4} + 5 q^{5} + 12 q^{8} - 2 q^{11} + 3 q^{13} + 6 q^{16} + 12 q^{17} - 3 q^{19} + 16 q^{20} + 15 q^{22} - 6 q^{25} + q^{26} + q^{29} + 6 q^{31} + 16 q^{32} - 3 q^{34} + 3 q^{37} - 8 q^{38} + 21 q^{40} + 22 q^{41} + 3 q^{43} + 23 q^{44} - 12 q^{46} - 18 q^{47} + 10 q^{50} + 3 q^{52} - 18 q^{53} + 12 q^{55} + 9 q^{58} - 18 q^{59} + 12 q^{61} - 36 q^{62} - 24 q^{64} + 10 q^{65} - 6 q^{68} - 18 q^{71} + 3 q^{73} + 6 q^{74} - 21 q^{76} + 30 q^{79} - 11 q^{80} + 9 q^{82} + 12 q^{83} - 9 q^{85} + 34 q^{86} + 21 q^{88} + 2 q^{89} + 15 q^{92} - 48 q^{94} - 32 q^{95} + 3 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.239123 0.169086 0.0845428 0.996420i \(-0.473057\pi\)
0.0845428 + 0.996420i \(0.473057\pi\)
\(3\) 0 0
\(4\) −1.94282 −0.971410
\(5\) −0.590972 1.02359i −0.264291 0.457765i 0.703087 0.711104i \(-0.251804\pi\)
−0.967378 + 0.253339i \(0.918471\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −0.942820 −0.333337
\(9\) 0 0
\(10\) −0.141315 0.244765i −0.0446878 0.0774015i
\(11\) −1.85185 + 3.20750i −0.558353 + 0.967096i 0.439281 + 0.898350i \(0.355233\pi\)
−0.997634 + 0.0687465i \(0.978100\pi\)
\(12\) 0 0
\(13\) 0.500000 0.866025i 0.138675 0.240192i −0.788320 0.615265i \(-0.789049\pi\)
0.926995 + 0.375073i \(0.122382\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 3.66019 0.915047
\(17\) 3.47141 + 6.01266i 0.841941 + 1.45828i 0.888252 + 0.459357i \(0.151920\pi\)
−0.0463112 + 0.998927i \(0.514747\pi\)
\(18\) 0 0
\(19\) 0.971410 1.68253i 0.222857 0.385999i −0.732818 0.680425i \(-0.761795\pi\)
0.955674 + 0.294426i \(0.0951285\pi\)
\(20\) 1.14815 + 1.98866i 0.256735 + 0.444677i
\(21\) 0 0
\(22\) −0.442820 + 0.766987i −0.0944096 + 0.163522i
\(23\) −2.80150 4.85235i −0.584154 1.01178i −0.994980 0.100071i \(-0.968093\pi\)
0.410826 0.911714i \(-0.365240\pi\)
\(24\) 0 0
\(25\) 1.80150 3.12030i 0.360301 0.624060i
\(26\) 0.119562 0.207087i 0.0234480 0.0406131i
\(27\) 0 0
\(28\) 0 0
\(29\) 0.119562 + 0.207087i 0.0222020 + 0.0384551i 0.876913 0.480649i \(-0.159599\pi\)
−0.854711 + 0.519104i \(0.826266\pi\)
\(30\) 0 0
\(31\) −1.66019 −0.298179 −0.149089 0.988824i \(-0.547634\pi\)
−0.149089 + 0.988824i \(0.547634\pi\)
\(32\) 2.76088 0.488059
\(33\) 0 0
\(34\) 0.830095 + 1.43777i 0.142360 + 0.246575i
\(35\) 0 0
\(36\) 0 0
\(37\) 4.77292 8.26693i 0.784662 1.35908i −0.144538 0.989499i \(-0.546170\pi\)
0.929201 0.369576i \(-0.120497\pi\)
\(38\) 0.232287 0.402332i 0.0376819 0.0652669i
\(39\) 0 0
\(40\) 0.557180 + 0.965064i 0.0880979 + 0.152590i
\(41\) 5.09097 8.81782i 0.795076 1.37711i −0.127715 0.991811i \(-0.540764\pi\)
0.922791 0.385301i \(-0.125903\pi\)
\(42\) 0 0
\(43\) −1.11273 1.92730i −0.169689 0.293910i 0.768622 0.639704i \(-0.220943\pi\)
−0.938311 + 0.345794i \(0.887610\pi\)
\(44\) 3.59781 6.23159i 0.542390 0.939447i
\(45\) 0 0
\(46\) −0.669905 1.16031i −0.0987721 0.171078i
\(47\) 5.82846 0.850168 0.425084 0.905154i \(-0.360245\pi\)
0.425084 + 0.905154i \(0.360245\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0.430782 0.746136i 0.0609217 0.105520i
\(51\) 0 0
\(52\) −0.971410 + 1.68253i −0.134710 + 0.233325i
\(53\) −5.80150 10.0485i −0.796898 1.38027i −0.921627 0.388077i \(-0.873139\pi\)
0.124729 0.992191i \(-0.460194\pi\)
\(54\) 0 0
\(55\) 4.37756 0.590270
\(56\) 0 0
\(57\) 0 0
\(58\) 0.0285900 + 0.0495193i 0.00375405 + 0.00650220i
\(59\) 2.60301 0.338883 0.169442 0.985540i \(-0.445804\pi\)
0.169442 + 0.985540i \(0.445804\pi\)
\(60\) 0 0
\(61\) 7.60301 0.973466 0.486733 0.873551i \(-0.338189\pi\)
0.486733 + 0.873551i \(0.338189\pi\)
\(62\) −0.396990 −0.0504178
\(63\) 0 0
\(64\) −6.66019 −0.832524
\(65\) −1.18194 −0.146602
\(66\) 0 0
\(67\) 3.50808 0.428580 0.214290 0.976770i \(-0.431256\pi\)
0.214290 + 0.976770i \(0.431256\pi\)
\(68\) −6.74433 11.6815i −0.817870 1.41659i
\(69\) 0 0
\(70\) 0 0
\(71\) −8.60301 −1.02099 −0.510495 0.859881i \(-0.670538\pi\)
−0.510495 + 0.859881i \(0.670538\pi\)
\(72\) 0 0
\(73\) 7.57442 + 13.1193i 0.886519 + 1.53550i 0.843963 + 0.536402i \(0.180217\pi\)
0.0425559 + 0.999094i \(0.486450\pi\)
\(74\) 1.14132 1.97682i 0.132675 0.229800i
\(75\) 0 0
\(76\) −1.88727 + 3.26886i −0.216485 + 0.374963i
\(77\) 0 0
\(78\) 0 0
\(79\) 7.37756 0.830040 0.415020 0.909812i \(-0.363775\pi\)
0.415020 + 0.909812i \(0.363775\pi\)
\(80\) −2.16307 3.74654i −0.241838 0.418876i
\(81\) 0 0
\(82\) 1.21737 2.10855i 0.134436 0.232850i
\(83\) 3.47141 + 6.01266i 0.381037 + 0.659975i 0.991211 0.132292i \(-0.0422338\pi\)
−0.610174 + 0.792267i \(0.708900\pi\)
\(84\) 0 0
\(85\) 4.10301 7.10662i 0.445034 0.770821i
\(86\) −0.266078 0.460861i −0.0286920 0.0496960i
\(87\) 0 0
\(88\) 1.74596 3.02409i 0.186120 0.322369i
\(89\) −1.37360 + 2.37915i −0.145602 + 0.252189i −0.929597 0.368577i \(-0.879845\pi\)
0.783996 + 0.620766i \(0.213178\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 5.44282 + 9.42724i 0.567453 + 0.982858i
\(93\) 0 0
\(94\) 1.39372 0.143751
\(95\) −2.29630 −0.235596
\(96\) 0 0
\(97\) 3.58414 + 6.20790i 0.363914 + 0.630317i 0.988601 0.150558i \(-0.0481069\pi\)
−0.624687 + 0.780875i \(0.714774\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −3.50000 + 6.06218i −0.350000 + 0.606218i
\(101\) 6.39248 11.0721i 0.636075 1.10171i −0.350211 0.936671i \(-0.613890\pi\)
0.986286 0.165044i \(-0.0527765\pi\)
\(102\) 0 0
\(103\) −2.19850 3.80791i −0.216624 0.375204i 0.737150 0.675730i \(-0.236171\pi\)
−0.953774 + 0.300526i \(0.902838\pi\)
\(104\) −0.471410 + 0.816506i −0.0462256 + 0.0800650i
\(105\) 0 0
\(106\) −1.38727 2.40283i −0.134744 0.233384i
\(107\) 6.86389 11.8886i 0.663557 1.14931i −0.316117 0.948720i \(-0.602379\pi\)
0.979674 0.200594i \(-0.0642873\pi\)
\(108\) 0 0
\(109\) −0.631600 1.09396i −0.0604963 0.104783i 0.834191 0.551476i \(-0.185935\pi\)
−0.894687 + 0.446693i \(0.852602\pi\)
\(110\) 1.04678 0.0998062
\(111\) 0 0
\(112\) 0 0
\(113\) 6.08126 10.5330i 0.572076 0.990866i −0.424276 0.905533i \(-0.639471\pi\)
0.996353 0.0853326i \(-0.0271953\pi\)
\(114\) 0 0
\(115\) −3.31122 + 5.73520i −0.308773 + 0.534810i
\(116\) −0.232287 0.402332i −0.0215673 0.0373556i
\(117\) 0 0
\(118\) 0.622440 0.0573003
\(119\) 0 0
\(120\) 0 0
\(121\) −1.35868 2.35331i −0.123517 0.213937i
\(122\) 1.81806 0.164599
\(123\) 0 0
\(124\) 3.22545 0.289654
\(125\) −10.1683 −0.909478
\(126\) 0 0
\(127\) 1.33981 0.118889 0.0594445 0.998232i \(-0.481067\pi\)
0.0594445 + 0.998232i \(0.481067\pi\)
\(128\) −7.11436 −0.628827
\(129\) 0 0
\(130\) −0.282630 −0.0247883
\(131\) 2.48345 + 4.30146i 0.216980 + 0.375820i 0.953883 0.300178i \(-0.0970461\pi\)
−0.736903 + 0.675998i \(0.763713\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.838864 0.0724668
\(135\) 0 0
\(136\) −3.27292 5.66886i −0.280650 0.486100i
\(137\) −2.16991 + 3.75839i −0.185387 + 0.321101i −0.943707 0.330782i \(-0.892687\pi\)
0.758320 + 0.651883i \(0.226021\pi\)
\(138\) 0 0
\(139\) 1.97141 3.41458i 0.167213 0.289621i −0.770226 0.637771i \(-0.779857\pi\)
0.937439 + 0.348150i \(0.113190\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −2.05718 −0.172635
\(143\) 1.85185 + 3.20750i 0.154859 + 0.268224i
\(144\) 0 0
\(145\) 0.141315 0.244765i 0.0117356 0.0203266i
\(146\) 1.81122 + 3.13713i 0.149898 + 0.259630i
\(147\) 0 0
\(148\) −9.27292 + 16.0612i −0.762229 + 1.32022i
\(149\) 5.55555 + 9.62249i 0.455128 + 0.788305i 0.998696 0.0510606i \(-0.0162602\pi\)
−0.543568 + 0.839365i \(0.682927\pi\)
\(150\) 0 0
\(151\) −6.96169 + 12.0580i −0.566535 + 0.981267i 0.430370 + 0.902652i \(0.358383\pi\)
−0.996905 + 0.0786145i \(0.974950\pi\)
\(152\) −0.915865 + 1.58632i −0.0742864 + 0.128668i
\(153\) 0 0
\(154\) 0 0
\(155\) 0.981125 + 1.69936i 0.0788059 + 0.136496i
\(156\) 0 0
\(157\) −0.0571799 −0.00456346 −0.00228173 0.999997i \(-0.500726\pi\)
−0.00228173 + 0.999997i \(0.500726\pi\)
\(158\) 1.76415 0.140348
\(159\) 0 0
\(160\) −1.63160 2.82601i −0.128989 0.223416i
\(161\) 0 0
\(162\) 0 0
\(163\) 0.754040 1.30604i 0.0590610 0.102297i −0.834983 0.550276i \(-0.814523\pi\)
0.894044 + 0.447979i \(0.147856\pi\)
\(164\) −9.89084 + 17.1314i −0.772345 + 1.33774i
\(165\) 0 0
\(166\) 0.830095 + 1.43777i 0.0644279 + 0.111592i
\(167\) 7.34213 12.7169i 0.568151 0.984067i −0.428598 0.903496i \(-0.640992\pi\)
0.996749 0.0805714i \(-0.0256745\pi\)
\(168\) 0 0
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) 0.981125 1.69936i 0.0752489 0.130335i
\(171\) 0 0
\(172\) 2.16182 + 3.74439i 0.164838 + 0.285507i
\(173\) 0.252796 0.0192197 0.00960987 0.999954i \(-0.496941\pi\)
0.00960987 + 0.999954i \(0.496941\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −6.77812 + 11.7400i −0.510920 + 0.884939i
\(177\) 0 0
\(178\) −0.328460 + 0.568910i −0.0246191 + 0.0426416i
\(179\) 7.09617 + 12.2909i 0.530393 + 0.918667i 0.999371 + 0.0354578i \(0.0112889\pi\)
−0.468978 + 0.883210i \(0.655378\pi\)
\(180\) 0 0
\(181\) 1.43147 0.106400 0.0532002 0.998584i \(-0.483058\pi\)
0.0532002 + 0.998584i \(0.483058\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 2.64132 + 4.57489i 0.194720 + 0.337266i
\(185\) −11.2826 −0.829515
\(186\) 0 0
\(187\) −25.7141 −1.88040
\(188\) −11.3236 −0.825862
\(189\) 0 0
\(190\) −0.549100 −0.0398359
\(191\) −15.0676 −1.09025 −0.545126 0.838354i \(-0.683518\pi\)
−0.545126 + 0.838354i \(0.683518\pi\)
\(192\) 0 0
\(193\) −7.84789 −0.564904 −0.282452 0.959282i \(-0.591148\pi\)
−0.282452 + 0.959282i \(0.591148\pi\)
\(194\) 0.857050 + 1.48445i 0.0615326 + 0.106578i
\(195\) 0 0
\(196\) 0 0
\(197\) −6.69002 −0.476644 −0.238322 0.971186i \(-0.576597\pi\)
−0.238322 + 0.971186i \(0.576597\pi\)
\(198\) 0 0
\(199\) −9.96978 17.2682i −0.706739 1.22411i −0.966060 0.258316i \(-0.916832\pi\)
0.259322 0.965791i \(-0.416501\pi\)
\(200\) −1.69850 + 2.94188i −0.120102 + 0.208022i
\(201\) 0 0
\(202\) 1.52859 2.64760i 0.107551 0.186284i
\(203\) 0 0
\(204\) 0 0
\(205\) −12.0345 −0.840525
\(206\) −0.525711 0.910559i −0.0366280 0.0634416i
\(207\) 0 0
\(208\) 1.83009 3.16982i 0.126894 0.219787i
\(209\) 3.59781 + 6.23159i 0.248866 + 0.431048i
\(210\) 0 0
\(211\) 9.04583 15.6678i 0.622741 1.07862i −0.366233 0.930523i \(-0.619353\pi\)
0.988973 0.148095i \(-0.0473141\pi\)
\(212\) 11.2713 + 19.5224i 0.774115 + 1.34081i
\(213\) 0 0
\(214\) 1.64132 2.84284i 0.112198 0.194333i
\(215\) −1.31518 + 2.27796i −0.0896944 + 0.155355i
\(216\) 0 0
\(217\) 0 0
\(218\) −0.151030 0.261592i −0.0102291 0.0177172i
\(219\) 0 0
\(220\) −8.50481 −0.573394
\(221\) 6.94282 0.467025
\(222\) 0 0
\(223\) −11.3285 19.6215i −0.758610 1.31395i −0.943560 0.331203i \(-0.892546\pi\)
0.184950 0.982748i \(-0.440788\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1.45417 2.51870i 0.0967299 0.167541i
\(227\) 2.64132 4.57489i 0.175310 0.303646i −0.764958 0.644080i \(-0.777240\pi\)
0.940269 + 0.340433i \(0.110574\pi\)
\(228\) 0 0
\(229\) 9.66827 + 16.7459i 0.638897 + 1.10660i 0.985675 + 0.168655i \(0.0539425\pi\)
−0.346778 + 0.937947i \(0.612724\pi\)
\(230\) −0.791790 + 1.37142i −0.0522091 + 0.0904288i
\(231\) 0 0
\(232\) −0.112725 0.195246i −0.00740077 0.0128185i
\(233\) −8.49028 + 14.7056i −0.556217 + 0.963396i 0.441591 + 0.897217i \(0.354414\pi\)
−0.997808 + 0.0661796i \(0.978919\pi\)
\(234\) 0 0
\(235\) −3.44445 5.96597i −0.224691 0.389177i
\(236\) −5.05718 −0.329194
\(237\) 0 0
\(238\) 0 0
\(239\) 8.44282 14.6234i 0.546121 0.945909i −0.452415 0.891808i \(-0.649437\pi\)
0.998535 0.0541011i \(-0.0172293\pi\)
\(240\) 0 0
\(241\) 13.5728 23.5088i 0.874300 1.51433i 0.0167933 0.999859i \(-0.494654\pi\)
0.857507 0.514473i \(-0.172012\pi\)
\(242\) −0.324893 0.562732i −0.0208849 0.0361738i
\(243\) 0 0
\(244\) −14.7713 −0.945634
\(245\) 0 0
\(246\) 0 0
\(247\) −0.971410 1.68253i −0.0618093 0.107057i
\(248\) 1.56526 0.0993941
\(249\) 0 0
\(250\) −2.43147 −0.153780
\(251\) −19.0780 −1.20419 −0.602096 0.798424i \(-0.705668\pi\)
−0.602096 + 0.798424i \(0.705668\pi\)
\(252\) 0 0
\(253\) 20.7518 1.30466
\(254\) 0.320380 0.0201024
\(255\) 0 0
\(256\) 11.6192 0.726198
\(257\) 7.42107 + 12.8537i 0.462913 + 0.801790i 0.999105 0.0423070i \(-0.0134707\pi\)
−0.536191 + 0.844097i \(0.680137\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 2.29630 0.142411
\(261\) 0 0
\(262\) 0.593850 + 1.02858i 0.0366882 + 0.0635458i
\(263\) −3.87072 + 6.70429i −0.238679 + 0.413404i −0.960335 0.278847i \(-0.910048\pi\)
0.721656 + 0.692251i \(0.243381\pi\)
\(264\) 0 0
\(265\) −6.85705 + 11.8768i −0.421225 + 0.729584i
\(266\) 0 0
\(267\) 0 0
\(268\) −6.81557 −0.416327
\(269\) 0.755675 + 1.30887i 0.0460743 + 0.0798031i 0.888143 0.459567i \(-0.151996\pi\)
−0.842069 + 0.539371i \(0.818662\pi\)
\(270\) 0 0
\(271\) −10.9903 + 19.0357i −0.667612 + 1.15634i 0.310958 + 0.950424i \(0.399350\pi\)
−0.978570 + 0.205915i \(0.933983\pi\)
\(272\) 12.7060 + 22.0075i 0.770416 + 1.33440i
\(273\) 0 0
\(274\) −0.518875 + 0.898718i −0.0313464 + 0.0542935i
\(275\) 6.67223 + 11.5566i 0.402350 + 0.696892i
\(276\) 0 0
\(277\) 5.41423 9.37772i 0.325310 0.563453i −0.656265 0.754530i \(-0.727865\pi\)
0.981575 + 0.191077i \(0.0611982\pi\)
\(278\) 0.471410 0.816506i 0.0282733 0.0489708i
\(279\) 0 0
\(280\) 0 0
\(281\) −8.43831 14.6156i −0.503387 0.871892i −0.999992 0.00391559i \(-0.998754\pi\)
0.496605 0.867977i \(-0.334580\pi\)
\(282\) 0 0
\(283\) 15.3171 0.910508 0.455254 0.890362i \(-0.349549\pi\)
0.455254 + 0.890362i \(0.349549\pi\)
\(284\) 16.7141 0.991799
\(285\) 0 0
\(286\) 0.442820 + 0.766987i 0.0261845 + 0.0453529i
\(287\) 0 0
\(288\) 0 0
\(289\) −15.6014 + 27.0224i −0.917728 + 1.58955i
\(290\) 0.0337917 0.0585290i 0.00198432 0.00343694i
\(291\) 0 0
\(292\) −14.7157 25.4884i −0.861173 1.49160i
\(293\) 4.68482 8.11435i 0.273690 0.474045i −0.696114 0.717932i \(-0.745089\pi\)
0.969804 + 0.243886i \(0.0784224\pi\)
\(294\) 0 0
\(295\) −1.53831 2.66442i −0.0895636 0.155129i
\(296\) −4.50000 + 7.79423i −0.261557 + 0.453030i
\(297\) 0 0
\(298\) 1.32846 + 2.30096i 0.0769556 + 0.133291i
\(299\) −5.60301 −0.324030
\(300\) 0 0
\(301\) 0 0
\(302\) −1.66470 + 2.88335i −0.0957929 + 0.165918i
\(303\) 0 0
\(304\) 3.55555 6.15838i 0.203925 0.353208i
\(305\) −4.49316 7.78239i −0.257278 0.445618i
\(306\) 0 0
\(307\) −2.71410 −0.154902 −0.0774509 0.996996i \(-0.524678\pi\)
−0.0774509 + 0.996996i \(0.524678\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0.234610 + 0.406356i 0.0133249 + 0.0230795i
\(311\) −13.9806 −0.792765 −0.396383 0.918085i \(-0.629735\pi\)
−0.396383 + 0.918085i \(0.629735\pi\)
\(312\) 0 0
\(313\) 19.0539 1.07699 0.538495 0.842628i \(-0.318993\pi\)
0.538495 + 0.842628i \(0.318993\pi\)
\(314\) −0.0136731 −0.000771615
\(315\) 0 0
\(316\) −14.3333 −0.806309
\(317\) 4.01943 0.225754 0.112877 0.993609i \(-0.463993\pi\)
0.112877 + 0.993609i \(0.463993\pi\)
\(318\) 0 0
\(319\) −0.885640 −0.0495863
\(320\) 3.93598 + 6.81732i 0.220028 + 0.381100i
\(321\) 0 0
\(322\) 0 0
\(323\) 13.4887 0.750529
\(324\) 0 0
\(325\) −1.80150 3.12030i −0.0999295 0.173083i
\(326\) 0.180309 0.312304i 0.00998637 0.0172969i
\(327\) 0 0
\(328\) −4.79987 + 8.31362i −0.265028 + 0.459043i
\(329\) 0 0
\(330\) 0 0
\(331\) −12.3776 −0.680332 −0.340166 0.940365i \(-0.610483\pi\)
−0.340166 + 0.940365i \(0.610483\pi\)
\(332\) −6.74433 11.6815i −0.370143 0.641106i
\(333\) 0 0
\(334\) 1.75567 3.04092i 0.0960663 0.166392i
\(335\) −2.07318 3.59085i −0.113270 0.196189i
\(336\) 0 0
\(337\) −6.12997 + 10.6174i −0.333920 + 0.578367i −0.983277 0.182117i \(-0.941705\pi\)
0.649356 + 0.760484i \(0.275038\pi\)
\(338\) 1.43474 + 2.48504i 0.0780395 + 0.135168i
\(339\) 0 0
\(340\) −7.97141 + 13.8069i −0.432310 + 0.748784i
\(341\) 3.07442 5.32505i 0.166489 0.288368i
\(342\) 0 0
\(343\) 0 0
\(344\) 1.04910 + 1.81709i 0.0565637 + 0.0979711i
\(345\) 0 0
\(346\) 0.0604495 0.00324978
\(347\) −6.64979 −0.356979 −0.178490 0.983942i \(-0.557121\pi\)
−0.178490 + 0.983942i \(0.557121\pi\)
\(348\) 0 0
\(349\) 5.71737 + 9.90278i 0.306044 + 0.530083i 0.977493 0.210967i \(-0.0676613\pi\)
−0.671449 + 0.741050i \(0.734328\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −5.11273 + 8.85550i −0.272509 + 0.472000i
\(353\) 11.0978 19.2220i 0.590677 1.02308i −0.403465 0.914995i \(-0.632194\pi\)
0.994141 0.108087i \(-0.0344725\pi\)
\(354\) 0 0
\(355\) 5.08414 + 8.80598i 0.269838 + 0.467373i
\(356\) 2.66866 4.62226i 0.141439 0.244979i
\(357\) 0 0
\(358\) 1.69686 + 2.93905i 0.0896819 + 0.155334i
\(359\) −3.77812 + 6.54389i −0.199401 + 0.345373i −0.948334 0.317272i \(-0.897233\pi\)
0.748933 + 0.662646i \(0.230566\pi\)
\(360\) 0 0
\(361\) 7.61273 + 13.1856i 0.400670 + 0.693980i
\(362\) 0.342298 0.0179908
\(363\) 0 0
\(364\) 0 0
\(365\) 8.95254 15.5062i 0.468597 0.811634i
\(366\) 0 0
\(367\) −9.26157 + 16.0415i −0.483450 + 0.837360i −0.999819 0.0190063i \(-0.993950\pi\)
0.516370 + 0.856366i \(0.327283\pi\)
\(368\) −10.2540 17.7605i −0.534529 0.925831i
\(369\) 0 0
\(370\) −2.69794 −0.140259
\(371\) 0 0
\(372\) 0 0
\(373\) −7.83009 13.5621i −0.405427 0.702220i 0.588944 0.808174i \(-0.299544\pi\)
−0.994371 + 0.105954i \(0.966210\pi\)
\(374\) −6.14884 −0.317949
\(375\) 0 0
\(376\) −5.49519 −0.283393
\(377\) 0.239123 0.0123155
\(378\) 0 0
\(379\) 4.03775 0.207405 0.103703 0.994608i \(-0.466931\pi\)
0.103703 + 0.994608i \(0.466931\pi\)
\(380\) 4.46130 0.228860
\(381\) 0 0
\(382\) −3.60301 −0.184346
\(383\) −0.112725 0.195246i −0.00575998 0.00997659i 0.863131 0.504980i \(-0.168500\pi\)
−0.868891 + 0.495003i \(0.835167\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −1.87661 −0.0955171
\(387\) 0 0
\(388\) −6.96333 12.0608i −0.353510 0.612296i
\(389\) 12.6316 21.8786i 0.640448 1.10929i −0.344885 0.938645i \(-0.612082\pi\)
0.985333 0.170643i \(-0.0545844\pi\)
\(390\) 0 0
\(391\) 19.4503 33.6890i 0.983646 1.70373i
\(392\) 0 0
\(393\) 0 0
\(394\) −1.59974 −0.0805938
\(395\) −4.35993 7.55162i −0.219372 0.379963i
\(396\) 0 0
\(397\) −10.1505 + 17.5811i −0.509438 + 0.882372i 0.490503 + 0.871440i \(0.336813\pi\)
−0.999940 + 0.0109322i \(0.996520\pi\)
\(398\) −2.38401 4.12922i −0.119499 0.206979i
\(399\) 0 0
\(400\) 6.59385 11.4209i 0.329693 0.571044i
\(401\) −7.61273 13.1856i −0.380161 0.658459i 0.610924 0.791689i \(-0.290798\pi\)
−0.991085 + 0.133231i \(0.957465\pi\)
\(402\) 0 0
\(403\) −0.830095 + 1.43777i −0.0413500 + 0.0716203i
\(404\) −12.4194 + 21.5111i −0.617890 + 1.07022i
\(405\) 0 0
\(406\) 0 0
\(407\) 17.6774 + 30.6182i 0.876238 + 1.51769i
\(408\) 0 0
\(409\) −1.65692 −0.0819294 −0.0409647 0.999161i \(-0.513043\pi\)
−0.0409647 + 0.999161i \(0.513043\pi\)
\(410\) −2.87772 −0.142121
\(411\) 0 0
\(412\) 4.27128 + 7.39807i 0.210431 + 0.364477i
\(413\) 0 0
\(414\) 0 0
\(415\) 4.10301 7.10662i 0.201409 0.348850i
\(416\) 1.38044 2.39099i 0.0676816 0.117228i
\(417\) 0 0
\(418\) 0.860320 + 1.49012i 0.0420796 + 0.0728840i
\(419\) −16.6871 + 28.9030i −0.815220 + 1.41200i 0.0939492 + 0.995577i \(0.470051\pi\)
−0.909170 + 0.416426i \(0.863282\pi\)
\(420\) 0 0
\(421\) −9.12025 15.7967i −0.444494 0.769886i 0.553523 0.832834i \(-0.313283\pi\)
−0.998017 + 0.0629481i \(0.979950\pi\)
\(422\) 2.16307 3.74654i 0.105297 0.182379i
\(423\) 0 0
\(424\) 5.46978 + 9.47393i 0.265636 + 0.460095i
\(425\) 25.0150 1.21341
\(426\) 0 0
\(427\) 0 0
\(428\) −13.3353 + 23.0974i −0.644586 + 1.11646i
\(429\) 0 0
\(430\) −0.314490 + 0.544712i −0.0151660 + 0.0262684i
\(431\) 14.6413 + 25.3595i 0.705247 + 1.22152i 0.966602 + 0.256281i \(0.0824974\pi\)
−0.261355 + 0.965243i \(0.584169\pi\)
\(432\) 0 0
\(433\) 12.2449 0.588451 0.294226 0.955736i \(-0.404938\pi\)
0.294226 + 0.955736i \(0.404938\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.22708 + 2.12537i 0.0587667 + 0.101787i
\(437\) −10.8856 −0.520731
\(438\) 0 0
\(439\) 4.83173 0.230606 0.115303 0.993330i \(-0.463216\pi\)
0.115303 + 0.993330i \(0.463216\pi\)
\(440\) −4.12725 −0.196759
\(441\) 0 0
\(442\) 1.66019 0.0789672
\(443\) −1.24488 −0.0591461 −0.0295730 0.999563i \(-0.509415\pi\)
−0.0295730 + 0.999563i \(0.509415\pi\)
\(444\) 0 0
\(445\) 3.24704 0.153924
\(446\) −2.70890 4.69195i −0.128270 0.222170i
\(447\) 0 0
\(448\) 0 0
\(449\) −8.82846 −0.416641 −0.208320 0.978061i \(-0.566800\pi\)
−0.208320 + 0.978061i \(0.566800\pi\)
\(450\) 0 0
\(451\) 18.8554 + 32.6585i 0.887867 + 1.53783i
\(452\) −11.8148 + 20.4638i −0.555721 + 0.962537i
\(453\) 0 0
\(454\) 0.631600 1.09396i 0.0296425 0.0513422i
\(455\) 0 0
\(456\) 0 0
\(457\) −10.5081 −0.491547 −0.245774 0.969327i \(-0.579042\pi\)
−0.245774 + 0.969327i \(0.579042\pi\)
\(458\) 2.31191 + 4.00434i 0.108028 + 0.187111i
\(459\) 0 0
\(460\) 6.43310 11.1425i 0.299945 0.519520i
\(461\) −11.2758 19.5302i −0.525166 0.909614i −0.999570 0.0293073i \(-0.990670\pi\)
0.474404 0.880307i \(-0.342663\pi\)
\(462\) 0 0
\(463\) −5.19850 + 9.00406i −0.241595 + 0.418454i −0.961169 0.275962i \(-0.911004\pi\)
0.719574 + 0.694416i \(0.244337\pi\)
\(464\) 0.437618 + 0.757977i 0.0203159 + 0.0351882i
\(465\) 0 0
\(466\) −2.03022 + 3.51645i −0.0940483 + 0.162897i
\(467\) −6.65856 + 11.5330i −0.308121 + 0.533682i −0.977951 0.208833i \(-0.933034\pi\)
0.669830 + 0.742514i \(0.266367\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −0.823649 1.42660i −0.0379921 0.0658043i
\(471\) 0 0
\(472\) −2.45417 −0.112962
\(473\) 8.24239 0.378986
\(474\) 0 0
\(475\) −3.50000 6.06218i −0.160591 0.278152i
\(476\) 0 0
\(477\) 0 0
\(478\) 2.01887 3.49679i 0.0923412 0.159940i
\(479\) −7.26771 + 12.5880i −0.332070 + 0.575163i −0.982918 0.184046i \(-0.941080\pi\)
0.650847 + 0.759209i \(0.274414\pi\)
\(480\) 0 0
\(481\) −4.77292 8.26693i −0.217626 0.376940i
\(482\) 3.24557 5.62149i 0.147832 0.256052i
\(483\) 0 0
\(484\) 2.63968 + 4.57206i 0.119985 + 0.207821i
\(485\) 4.23624 7.33739i 0.192358 0.333174i
\(486\) 0 0
\(487\) −6.52696 11.3050i −0.295765 0.512279i 0.679398 0.733770i \(-0.262241\pi\)
−0.975162 + 0.221491i \(0.928908\pi\)
\(488\) −7.16827 −0.324492
\(489\) 0 0
\(490\) 0 0
\(491\) 9.67223 16.7528i 0.436502 0.756043i −0.560915 0.827873i \(-0.689551\pi\)
0.997417 + 0.0718303i \(0.0228840\pi\)
\(492\) 0 0
\(493\) −0.830095 + 1.43777i −0.0373856 + 0.0647538i
\(494\) −0.232287 0.402332i −0.0104511 0.0181018i
\(495\) 0 0
\(496\) −6.07661 −0.272848
\(497\) 0 0
\(498\) 0 0
\(499\) 18.1111 + 31.3693i 0.810764 + 1.40428i 0.912330 + 0.409455i \(0.134281\pi\)
−0.101566 + 0.994829i \(0.532385\pi\)
\(500\) 19.7551 0.883476
\(501\) 0 0
\(502\) −4.56199 −0.203612
\(503\) 15.6764 0.698974 0.349487 0.936941i \(-0.386356\pi\)
0.349487 + 0.936941i \(0.386356\pi\)
\(504\) 0 0
\(505\) −15.1111 −0.672435
\(506\) 4.96225 0.220599
\(507\) 0 0
\(508\) −2.60301 −0.115490
\(509\) −17.1517 29.7076i −0.760237 1.31677i −0.942729 0.333561i \(-0.891750\pi\)
0.182492 0.983207i \(-0.441584\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 17.0071 0.751616
\(513\) 0 0
\(514\) 1.77455 + 3.07361i 0.0782720 + 0.135571i
\(515\) −2.59850 + 4.50073i −0.114503 + 0.198326i
\(516\) 0 0
\(517\) −10.7934 + 18.6948i −0.474694 + 0.822195i
\(518\) 0 0
\(519\) 0 0
\(520\) 1.11436 0.0488679
\(521\) 5.12244 + 8.87233i 0.224418 + 0.388704i 0.956145 0.292895i \(-0.0946185\pi\)
−0.731727 + 0.681598i \(0.761285\pi\)
\(522\) 0 0
\(523\) 15.3015 26.5030i 0.669088 1.15889i −0.309071 0.951039i \(-0.600018\pi\)
0.978159 0.207856i \(-0.0666485\pi\)
\(524\) −4.82489 8.35696i −0.210776 0.365075i
\(525\) 0 0
\(526\) −0.925580 + 1.60315i −0.0403572 + 0.0699007i
\(527\) −5.76320 9.98215i −0.251049 0.434829i
\(528\) 0 0
\(529\) −4.19686 + 7.26918i −0.182472 + 0.316051i
\(530\) −1.63968 + 2.84001i −0.0712232 + 0.123362i
\(531\) 0 0
\(532\) 0 0
\(533\) −5.09097 8.81782i −0.220514 0.381942i
\(534\) 0 0
\(535\) −16.2255 −0.701487
\(536\) −3.30749 −0.142862
\(537\) 0 0
\(538\) 0.180699 + 0.312981i 0.00779051 + 0.0134936i
\(539\) 0 0
\(540\) 0 0
\(541\) 13.0458 22.5960i 0.560884 0.971480i −0.436536 0.899687i \(-0.643795\pi\)
0.997420 0.0717926i \(-0.0228720\pi\)
\(542\) −2.62803 + 4.55189i −0.112884 + 0.195520i
\(543\) 0 0
\(544\) 9.58414 + 16.6002i 0.410916 + 0.711728i
\(545\) −0.746515 + 1.29300i −0.0319772 + 0.0553861i
\(546\) 0 0
\(547\) 5.46169 + 9.45993i 0.233525 + 0.404478i 0.958843 0.283937i \(-0.0916405\pi\)
−0.725318 + 0.688414i \(0.758307\pi\)
\(548\) 4.21574 7.30187i 0.180087 0.311920i
\(549\) 0 0
\(550\) 1.59549 + 2.76346i 0.0680317 + 0.117834i
\(551\) 0.464574 0.0197915
\(552\) 0 0
\(553\) 0 0
\(554\) 1.29467 2.24243i 0.0550052 0.0952718i
\(555\) 0 0
\(556\) −3.83009 + 6.63392i −0.162432 + 0.281341i
\(557\) −6.97210 12.0760i −0.295417 0.511678i 0.679665 0.733523i \(-0.262125\pi\)
−0.975082 + 0.221845i \(0.928792\pi\)
\(558\) 0 0
\(559\) −2.22545 −0.0941265
\(560\) 0 0
\(561\) 0 0
\(562\) −2.01780 3.49492i −0.0851156 0.147424i
\(563\) 30.2574 1.27520 0.637600 0.770368i \(-0.279927\pi\)
0.637600 + 0.770368i \(0.279927\pi\)
\(564\) 0 0
\(565\) −14.3754 −0.604778
\(566\) 3.66268 0.153954
\(567\) 0 0
\(568\) 8.11109 0.340334
\(569\) 21.1352 0.886032 0.443016 0.896514i \(-0.353908\pi\)
0.443016 + 0.896514i \(0.353908\pi\)
\(570\) 0 0
\(571\) −32.7863 −1.37207 −0.686033 0.727571i \(-0.740649\pi\)
−0.686033 + 0.727571i \(0.740649\pi\)
\(572\) −3.59781 6.23159i −0.150432 0.260556i
\(573\) 0 0
\(574\) 0 0
\(575\) −20.1877 −0.841885
\(576\) 0 0
\(577\) −8.68715 15.0466i −0.361651 0.626397i 0.626582 0.779355i \(-0.284453\pi\)
−0.988233 + 0.152958i \(0.951120\pi\)
\(578\) −3.73065 + 6.46168i −0.155175 + 0.268770i
\(579\) 0 0
\(580\) −0.274550 + 0.475534i −0.0114001 + 0.0197455i
\(581\) 0 0
\(582\) 0 0
\(583\) 42.9740 1.77980
\(584\) −7.14132 12.3691i −0.295510 0.511838i
\(585\) 0 0
\(586\) 1.12025 1.94033i 0.0462771 0.0801543i
\(587\) −8.48796 14.7016i −0.350336 0.606799i 0.635973 0.771712i \(-0.280599\pi\)
−0.986308 + 0.164913i \(0.947266\pi\)
\(588\) 0 0
\(589\) −1.61273 + 2.79332i −0.0664512 + 0.115097i
\(590\) −0.367845 0.637125i −0.0151439 0.0262300i
\(591\) 0 0
\(592\) 17.4698 30.2585i 0.718003 1.24362i
\(593\) 6.53667 11.3218i 0.268429 0.464932i −0.700027 0.714116i \(-0.746829\pi\)
0.968456 + 0.249184i \(0.0801622\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −10.7934 18.6948i −0.442116 0.765767i
\(597\) 0 0
\(598\) −1.33981 −0.0547889
\(599\) −29.2060 −1.19333 −0.596663 0.802492i \(-0.703507\pi\)
−0.596663 + 0.802492i \(0.703507\pi\)
\(600\) 0 0
\(601\) 3.89536 + 6.74695i 0.158895 + 0.275214i 0.934470 0.356041i \(-0.115874\pi\)
−0.775576 + 0.631255i \(0.782540\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 13.5253 23.4265i 0.550337 0.953212i
\(605\) −1.60589 + 2.78148i −0.0652887 + 0.113083i
\(606\) 0 0
\(607\) −9.82038 17.0094i −0.398597 0.690390i 0.594956 0.803758i \(-0.297169\pi\)
−0.993553 + 0.113368i \(0.963836\pi\)
\(608\) 2.68194 4.64526i 0.108767 0.188390i
\(609\) 0 0
\(610\) −1.07442 1.86095i −0.0435020 0.0753477i
\(611\) 2.91423 5.04759i 0.117897 0.204204i
\(612\) 0 0
\(613\) −11.7826 20.4081i −0.475896 0.824276i 0.523723 0.851889i \(-0.324543\pi\)
−0.999619 + 0.0276128i \(0.991209\pi\)
\(614\) −0.649005 −0.0261917
\(615\) 0 0
\(616\) 0 0
\(617\) −5.33009 + 9.23200i −0.214582 + 0.371666i −0.953143 0.302520i \(-0.902172\pi\)
0.738562 + 0.674186i \(0.235505\pi\)
\(618\) 0 0
\(619\) −9.00752 + 15.6015i −0.362043 + 0.627077i −0.988297 0.152542i \(-0.951254\pi\)
0.626254 + 0.779619i \(0.284587\pi\)
\(620\) −1.90615 3.30155i −0.0765528 0.132593i
\(621\) 0 0
\(622\) −3.34308 −0.134045
\(623\) 0 0
\(624\) 0 0
\(625\) −2.99837 5.19332i −0.119935 0.207733i
\(626\) 4.55623 0.182104
\(627\) 0 0
\(628\) 0.111090 0.00443299
\(629\) 66.2750 2.64256
\(630\) 0 0
\(631\) 12.4703 0.496436 0.248218 0.968704i \(-0.420155\pi\)
0.248218 + 0.968704i \(0.420155\pi\)
\(632\) −6.95571 −0.276683
\(633\) 0 0
\(634\) 0.961139 0.0381717
\(635\) −0.791790 1.37142i −0.0314212 0.0544232i
\(636\) 0 0
\(637\) 0 0
\(638\) −0.211777 −0.00838434
\(639\) 0 0
\(640\) 4.20439 + 7.28221i 0.166193 + 0.287855i
\(641\) 9.57279 16.5806i 0.378102 0.654892i −0.612684 0.790328i \(-0.709910\pi\)
0.990786 + 0.135436i \(0.0432434\pi\)
\(642\) 0 0
\(643\) 3.24433 5.61934i 0.127944 0.221605i −0.794936 0.606693i \(-0.792496\pi\)
0.922880 + 0.385088i \(0.125829\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 3.22545 0.126904
\(647\) 24.0494 + 41.6548i 0.945479 + 1.63762i 0.754789 + 0.655968i \(0.227739\pi\)
0.190691 + 0.981650i \(0.438927\pi\)
\(648\) 0 0
\(649\) −4.82038 + 8.34914i −0.189216 + 0.327733i
\(650\) −0.430782 0.746136i −0.0168967 0.0292659i
\(651\) 0 0
\(652\) −1.46496 + 2.53739i −0.0573724 + 0.0993720i
\(653\) −21.6202 37.4474i −0.846066 1.46543i −0.884692 0.466175i \(-0.845632\pi\)
0.0386267 0.999254i \(-0.487702\pi\)
\(654\) 0 0
\(655\) 2.93530 5.08408i 0.114691 0.198651i
\(656\) 18.6339 32.2749i 0.727532 1.26012i
\(657\) 0 0
\(658\) 0 0
\(659\) −1.25404 2.17206i −0.0488505 0.0846115i 0.840566 0.541709i \(-0.182222\pi\)
−0.889417 + 0.457097i \(0.848889\pi\)
\(660\) 0 0
\(661\) 42.3354 1.64666 0.823329 0.567565i \(-0.192114\pi\)
0.823329 + 0.567565i \(0.192114\pi\)
\(662\) −2.95976 −0.115034
\(663\) 0 0
\(664\) −3.27292 5.66886i −0.127014 0.219994i
\(665\) 0 0
\(666\) 0 0
\(667\) 0.669905 1.16031i 0.0259388 0.0449274i
\(668\) −14.2644 + 24.7067i −0.551908 + 0.955933i
\(669\) 0 0
\(670\) −0.495745 0.858655i −0.0191523 0.0331727i
\(671\) −14.0796 + 24.3866i −0.543538 + 0.941435i
\(672\) 0 0
\(673\) −6.70765 11.6180i −0.258561 0.447841i 0.707296 0.706918i \(-0.249915\pi\)
−0.965857 + 0.259077i \(0.916582\pi\)
\(674\) −1.46582 + 2.53887i −0.0564612 + 0.0977936i
\(675\) 0 0
\(676\) −11.6569 20.1904i −0.448343 0.776553i
\(677\) 1.96225 0.0754154 0.0377077 0.999289i \(-0.487994\pi\)
0.0377077 + 0.999289i \(0.487994\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −3.86840 + 6.70027i −0.148346 + 0.256943i
\(681\) 0 0
\(682\) 0.735165 1.27334i 0.0281509 0.0487589i
\(683\) 13.5836 + 23.5275i 0.519761 + 0.900253i 0.999736 + 0.0229706i \(0.00731243\pi\)
−0.479975 + 0.877282i \(0.659354\pi\)
\(684\) 0 0
\(685\) 5.12941 0.195985
\(686\) 0 0
\(687\) 0 0
\(688\) −4.07279 7.05427i −0.155273 0.268942i
\(689\) −11.6030 −0.442039
\(690\) 0 0
\(691\) 50.3171 1.91415 0.957077 0.289835i \(-0.0936005\pi\)
0.957077 + 0.289835i \(0.0936005\pi\)
\(692\) −0.491138 −0.0186703
\(693\) 0 0
\(694\) −1.59012 −0.0603601
\(695\) −4.66019 −0.176771
\(696\) 0 0
\(697\) 70.6914 2.67763
\(698\) 1.36716 + 2.36798i 0.0517476 + 0.0896295i
\(699\) 0 0
\(700\) 0 0
\(701\) −45.1672 −1.70594 −0.852970 0.521960i \(-0.825201\pi\)
−0.852970 + 0.521960i \(0.825201\pi\)
\(702\) 0 0
\(703\) −9.27292 16.0612i −0.349735 0.605758i
\(704\) 12.3337 21.3625i 0.464842 0.805131i
\(705\) 0 0
\(706\) 2.65374 4.59642i 0.0998750 0.172989i
\(707\) 0 0
\(708\) 0 0
\(709\) 39.6181 1.48789 0.743944 0.668242i \(-0.232953\pi\)
0.743944 + 0.668242i \(0.232953\pi\)
\(710\) 1.21574 + 2.10571i 0.0456257 + 0.0790261i
\(711\) 0 0
\(712\) 1.29506 2.24311i 0.0485344 0.0840640i
\(713\) 4.65103 + 8.05582i 0.174182 + 0.301693i
\(714\) 0 0
\(715\) 2.18878 3.79108i 0.0818557 0.141778i
\(716\) −13.7866 23.8791i −0.515229 0.892403i
\(717\) 0 0
\(718\) −0.903436 + 1.56480i −0.0337159 + 0.0583977i
\(719\) 11.0189 19.0853i 0.410935 0.711760i −0.584058 0.811712i \(-0.698536\pi\)
0.994992 + 0.0999525i \(0.0318691\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.82038 + 3.15299i 0.0677475 + 0.117342i
\(723\) 0 0
\(724\) −2.78109 −0.103358
\(725\) 0.861564 0.0319977
\(726\) 0 0
\(727\) 14.0555 + 24.3449i 0.521291 + 0.902903i 0.999693 + 0.0247621i \(0.00788284\pi\)
−0.478402 + 0.878141i \(0.658784\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 2.14076 3.70790i 0.0792331 0.137236i
\(731\) 7.72545 13.3809i 0.285736 0.494909i
\(732\) 0 0
\(733\) 5.93474 + 10.2793i 0.219205 + 0.379674i 0.954565 0.298003i \(-0.0963204\pi\)
−0.735360 + 0.677676i \(0.762987\pi\)
\(734\) −2.21466 + 3.83590i −0.0817444 + 0.141586i
\(735\) 0 0
\(736\) −7.73461 13.3967i −0.285102 0.493810i
\(737\) −6.49643 + 11.2522i −0.239299 + 0.414478i
\(738\) 0 0
\(739\) 6.09222 + 10.5520i 0.224106 + 0.388163i 0.956051 0.293201i \(-0.0947206\pi\)
−0.731945 + 0.681364i \(0.761387\pi\)
\(740\) 21.9201 0.805800
\(741\) 0 0
\(742\) 0 0
\(743\) −22.2427 + 38.5255i −0.816005 + 1.41336i 0.0925987 + 0.995704i \(0.470483\pi\)
−0.908604 + 0.417659i \(0.862851\pi\)
\(744\) 0 0
\(745\) 6.56634 11.3732i 0.240572 0.416683i
\(746\) −1.87236 3.24302i −0.0685519 0.118735i
\(747\) 0 0
\(748\) 49.9579 1.82664
\(749\) 0 0
\(750\) 0 0
\(751\) −21.4029 37.0709i −0.781002 1.35274i −0.931358 0.364104i \(-0.881375\pi\)
0.150356 0.988632i \(-0.451958\pi\)
\(752\) 21.3333 0.777944
\(753\) 0 0
\(754\) 0.0571799 0.00208237
\(755\) 16.4567 0.598919
\(756\) 0 0
\(757\) −22.4919 −0.817483 −0.408741 0.912650i \(-0.634032\pi\)
−0.408741 + 0.912650i \(0.634032\pi\)
\(758\) 0.965520 0.0350693
\(759\) 0 0
\(760\) 2.16500 0.0785328
\(761\) 7.16827 + 12.4158i 0.259850 + 0.450073i 0.966201 0.257788i \(-0.0829937\pi\)
−0.706352 + 0.707861i \(0.749660\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 29.2736 1.05908
\(765\) 0 0
\(766\) −0.0269552 0.0466878i −0.000973931 0.00168690i
\(767\) 1.30150 2.25427i 0.0469946 0.0813971i
\(768\) 0 0
\(769\) −15.6105 + 27.0382i −0.562930 + 0.975024i 0.434309 + 0.900764i \(0.356993\pi\)
−0.997239 + 0.0742597i \(0.976341\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 15.2470 0.548753
\(773\) −2.19002 3.79323i −0.0787697 0.136433i 0.823950 0.566663i \(-0.191766\pi\)
−0.902719 + 0.430230i \(0.858433\pi\)
\(774\) 0 0
\(775\) −2.99084 + 5.18029i −0.107434 + 0.186081i
\(776\) −3.37919 5.85294i −0.121306 0.210108i
\(777\) 0 0
\(778\) 3.02051 5.23168i 0.108291 0.187565i
\(779\) −9.89084 17.1314i −0.354376 0.613798i
\(780\) 0 0
\(781\) 15.9315 27.5941i 0.570073 0.987395i
\(782\) 4.65103 8.05582i 0.166321 0.288076i
\(783\) 0 0
\(784\) 0 0
\(785\) 0.0337917 + 0.0585290i 0.00120608 + 0.00208899i
\(786\) 0 0
\(787\) −27.6213